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In recent years, the sparsity-promoting reconstruction method based on the compressed sensing theory has been rapidly developed and applied to seismic data reconstruction. Many achievements have been made toward providing high-quality reconstruction by using undersampled data. However, the problem of insufficient reconstruction in null traces still hinders us a lot in practical applications, especially for complex seismic data. Aiming to solve this problem, we made full use of the sparsity characteristics of seismic data in multiple sparse transform domains and jointly reconstructed seismic data to realize the complementary advantages of multiple sparse transforms; As such, we propose a high-precision seismic data recovery method with multi-domain sparsity constraints based on curvelet and high-resolution Radon transforms . Numerical examples by synthetic and real data showed that the new approach can achieve a better reconstruction result than the commonly used curvelet-based recovery method. Integrated with the curvelet transform to develop new recovery method, the high-resolution Radon transform has more advantages than the conventional Radon transform for overcoming the shortcomings associated with the insufficient reconstruction of high-amplitude events. At the same time, the method is also applicable for developing new reconstruction methods by combining other sparse transforms depending on the characteristics of seismic data. The reconstruction method with multi-domain sparsity constraints can easily be extended to three-dimensional situation.